GCSE Solving Quadratic Equations 5 — Questions and Answers
Question 1: What is the axis of symmetry of the parabola y = 2x² − 8x + 3?
- x = 2 (Correct answer)
- x = −2
- x = 4
- x = −4
Correct answer: x = 2
Axis of symmetry: x = −b/(2a) = 8/4 = 2.
Question 2: Solve x² − 2x − 8 = 0 using the quadratic formula.
- x = 4 and x = −2 (Correct answer)
- x = −4 and x = 2
- x = 4 and x = 2
- x = −4 and x = −2
Correct answer: x = 4 and x = −2
x = (2 ± √36) / 2 = (2 ± 6) / 2, giving x = 4 or x = −2.
Question 3: If the roots of a quadratic are x = 5 and x = −3, which equation fits?
- x² − 2x − 15 = 0 (Correct answer)
- x² + 2x − 15 = 0
- x² − 2x + 15 = 0
- x² + 2x + 15 = 0
Correct answer: x² − 2x − 15 = 0
Sum of roots = 2, product = −15, so the equation is x² − 2x − 15 = 0.
Question 4: Solve (x − 3)² = 25.
- x = 8 and x = −2 (Correct answer)
- x = 8 and x = 2
- x = −8 and x = 2
- x = 28 and x = −22
Correct answer: x = 8 and x = −2
x − 3 = ±5, so x = 8 or x = −2.
Question 5: Which quadratic equation has roots that are both negative?
- x² + 5x + 6 = 0 (Correct answer)
- x² − 5x + 6 = 0
- x² + x − 6 = 0
- x² − x − 6 = 0
Correct answer: x² + 5x + 6 = 0
x² + 5x + 6 = (x + 2)(x + 3) = 0 gives x = −2 and x = −3, both negative.
Question 6: A quadratic has the form x² + px + q = 0. If the discriminant is zero, which statement is true?
- The equation has exactly one solution (Correct answer)
- The equation has two distinct solutions
- The equation has no real solutions
- The equation has infinitely many solutions
Correct answer: The equation has exactly one solution
A zero discriminant means the quadratic is a perfect square with exactly one repeated root.
Question 7: Solve 6x² − x − 2 = 0 by factoring.
- x = ⅔ and x = −½ (Correct answer)
- x = −⅔ and x = ½
- x = ⅔ and x = ½
- x = −⅔ and x = −½
Correct answer: x = ⅔ and x = −½
Factoring gives (3x − 2)(2x + 1) = 0, so x = ⅔ or x = −½.
GCSE Solving Quadratic Equations 5
What is the axis of symmetry of the parabola y = 2x² − 8x + 3?